Rep-tiling Euclidean space

  • Andrew Vince
Chapter

Summary

A rep-tiling. T is a self replicating, lattice tiling of R n . Lattice tiling means a tiling by translates of a single compact tile by the points of a lattice, and self-replicating means that there is a non-singular linear map Ø: R n → R n such that, for each T ∈T, the image Ø(T) is, in turn, tiled by T. This topic has recently come under investigation, not only because of its recreational appeal, but because of its application to the theory of wavelets and to computer addressing. The paper presents an exposition of some recent results on rep-tiling, including a construction of essentially all rep-tilings of Euclidean space. The construction is based on radix representation of points of a lattice. One particular radix representation, called the generalized balanced ternary, is singled out as an example because of its relevance to the field of computer vision.

Keywords

Lattice Point Voronoi Cell Iterate Function System Voronoi Region Crystallographic Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Birkhäuser Verlag Basel 1995

Authors and Affiliations

  • Andrew Vince
    • 1
  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA

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